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On the fakeness of fake supergravity

Alessio Celi1,*, Anna Ceresole2,†, Gianguido Dall’Agata3,‡, Antoine Van Proeyen1,§, and Marco Zagermann4,∥

  • 1Instituut voor Theoretische Fysica, Katholieke Universiteit Leuven, Celestijnenlaan 200D B-3001 Leuven, Belgium
  • 2INFN, Sezione di Torino and Dipartimento di Fisica Teorica, Università di Torino, Via P. Giuria 1, I-10125 Torino, Italy
  • 3Institut für Physik, Humboldt Universität, Newtonstrasse 15, 12489 Adlershof, Berlin, Germany. From 1st October: Theory Unit, CERN, Geneva 23, CH1211, Switzerland
  • 4Department of Physics, Stanford University, Varian Building, Stanford, California 94305-4060, USA

  • *Electronic address: Alessio.Celi@fys.kuleuven.ac.be
  • †Electronic address: ceresole@to.infn.it
  • ‡Electronic address: Gianguido.Dall’Agata@cern.ch
  • §Electronic address: Antoine.VanProeyen@fys.kuleuven.ac.be
  • ∥Electronic address: zagermann@itp.stanford.edu
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Phys. Rev. D 71, 045009 – Published 14 February, 2005

DOI: https://doi.org/10.1103/PhysRevD.71.045009

Abstract

We revisit and complete the study of curved BPS-domain walls in matter-coupled 5D, N=2 supergravity and carefully analyze the relation to gravitational theories known as “fake supergravities.” We first show that curved BPS-domain walls require the presence of nontrivial hypermultiplet scalars, whereas walls that are solely supported by vector multiplet scalars are necessarily flat, due to the constraints from very special geometry. We then recover fake supergravity as the effective description of true supergravity where one restricts the attention to the flowing scalar field of a given BPS-domain wall. In general, however, true supergravity can be simulated by fake supergravity at most locally, based upon two choices: (i) a suitable adapted coordinate system on the scalar manifold, such that only one scalar field plays a dynamical role, and (ii) a gauge fixing of the SU(2) connection on the quaternionic-Kähler manifold, as this connection does not fit the simple formalism of fake supergravity. Employing these gauge and coordinate choices, the BPS-equations for both vector and hypermultiplet scalars become identical to the fake supergravity equations, once the line of flow is determined by the full supergravity equations.

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Phys. Rev. D 71, 045009– Published 14 February, 2005
  • Received 18 October 2004

© 2005 American Physical Society

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